Phasegram Analysis of Vocal Fold Vibration Documented With Laryngeal High-speed Video Endoscopy

Summary

Introduction

In a recent publication, the phasegram, a bifurcation diagram over time, has been introduced as an intuitive visualization tool for assessing the vibratory states of oscillating systems. Here, this nonlinear dynamics approach is augmented with quantitative analysis parameters, and it is applied to clinical laryngeal high-speed video (HSV) endoscopic recordings of healthy and pathological phonations.

Methods

HSV data from a total of 73 females diagnosed as healthy (n = 42), or with functional dysphonia (n = 15) or with unilateral vocal fold paralysis (n = 16), were quantitatively analyzed. Glottal area waveforms (GAW) and left and right hemi-GAWs (hGAW) were extracted from the HSV recordings. Based on Poincaré sections through phase space-embedded signals, two novel quantitative parameters were computed: the phasegram entropy (PE) and the phasegram complexity estimate (PCE), inspired by signal entropy and correlation dimension computation, respectively.

Results

Both PE and PCE assumed higher average values (suggesting more irregular vibrations) for the pathological as compared with the healthy participants, thus significantly discriminating healthy group from the paralysis group (P = 0.02 for both PE and PCE). Comparisons of individual PE or PCE data for the left and the right hGAW within each subject resulted in asymmetry measures for the regularity of vocal fold vibration. The PCE-based asymmetry measure revealed significant differences between the healthy group and the paralysis group (P = 0.03).

Conclusions

Quantitative phasegram analysis of GAW and hGAW data is a promising tool for the automated processing of HSV data in research and in clinical practice.

Introduction

The behavior of a vibratory system is periodic if the observed oscillatory pattern continuously repeats itself after a constant time interval. Periodicity abiding this strict definition is hardly observed in empirical data of biomechanical systems such as the voice. Rather, voice production is at best a nearly periodic¹ phenomenon under nonpathological conditions. In the presence of a voice disorder, vocal fold vibration and thus the generated acoustical output is likely to be more or less perturbed,² often caused by highly irregular vibratory regimes of the vocal folds.3, 4, 5, 6

Deviations of periodicity can be quantified in a variety of ways. Apart from time domain-based and frequency domain-based approaches such as calculation of jitter⁷ or the harmonics-to-noise ratio,⁸ methods from nonlinear systems analysis have received growing interest in the past decades.9, 10, 11, 12 In non-linear dynamics methods, the voice is considered to be a dynamical system¹³ that is able to exhibit a wide variety of oscillatory behavior “on the way to chaos.”14, 15

Several quantitative methods for assessing the complexity of the temporal behavior of nonlinear systems have been introduced in the domain of mathematics and physics, for instance the correlation dimension,¹⁶ Lyapunov exponents,¹⁷ or Tokuda et al's low-dimensional nonlinearity measure.¹⁸ These methods have been successfully applied during the analysis of biosignals from both healthy and pathological voices, such as the acoustical waveform,12, 19, 20, 21, 22 electroglottography,23, 24, 25 or data derived from high-speed video (HSV) recordings of vocal fold vibration.26, 27, 28, 29

The detailed interpretation of available quantitative methods for analyzing the dynamics of irregular voice often requires expert background knowledge in mathematics and physics. In contrast, visualization methods are often easier to understand for nonexperts. Such visualization methods, applied to nonperiodic voice production, include for example spectrograms12, 30, 31 or local maxima displays.³²

Recently, a novel visualization method of system dynamics has been introduced: the phasegram.³³ In a phasegram, time is mapped onto the x-axis, and various vibratory regimes, such as periodic oscillation, subharmonics, or chaos, are identified within the generated graph by the number and the stability of horizontal lines. Phasegrams can be interpreted as bifurcation diagrams in time. They are particularly suited for nonstationary signals. The benefits of sliding window analysis are combined with the visualization potential of phase space embedding.34, 35 In contrast to other nonlinear analysis techniques (eg, bifurcation maps), phasegrams can be automatically constructed from a time domain signal alone, no additional system parameter needs to be known. In contrast to conventional voice perturbation measures (eg, jitter), no information about glottal cycle duration or fundamental frequency needs to be known.

Phasegrams have thus far been utilized for the visualization³³ and the manual classification³⁶ of electroglottographic voice signals. Here, their application to the analysis of time series data derived from HSV recordings is introduced by example of simulated vocal fold vibrations using a lumped element biomechanical model. The concept is further extended to healthy and pathological phonations, considering both stationary and nonstationary signals. The analysis is complemented by spatiotemporal visualization37, 38 and of Fourier analysis of vocal fold vibration and of simultaneously acquired acoustical signals. It will be shown that sequences of aberrant vocal fold vibratory behavior can be easily located in phasegrams, thus earmarking the method as a promising candidate for detection of clinically relevant passages within HSV recordings. To facilitate automated objective analysis of vocal fold vibratory behavior (as seen in HSV recordings), two novel quantitative analysis parameters derived from the phasegram visualization are introduced in this paper. The performance of these quantitative parameters is assessed through analysis of a database containing HSV recordings of healthy and pathological phonations.